We study an extended SU(N) single-impurity Kondo model in which the impurityspin is described by a combination of Abrikosov fermions and Schwinger bosons.Our aim is to describe both the quasiparticle-like excitations and the locallycritical modes observed in various physical situations, including non-Fermiliquid (NFL) behavior in heavy fermions in the vicinity of a quantum criticalpoint and anomalous transport properties in quantum wires. In contrast withmodels with either pure bosonic or pure fermionic impurities, the strongcoupling fixed point is unstable against the conduction electron kinetic termunder certain conditions. The stability region of the strong coupling fixedpoint coincides with the region where the partially screened, effectiveimpurity repels the electrons on adjacent sites. In the instability region, theimpurity tends to attract $(N-1)$ electrons to the neighboring sites, givingrise to a double-stage Kondo effect with additional screening of the impurity.
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